arXiv subjects

Jose Rodriguez

Publications and source records attributed to Jose Rodriguez.

17 recordsLinked to original sources

arXiv2026

Grouping Auction-Consensus Algorithm for Decentralized Task Allocation in Multi-Robot Systems

Decentralized multi-robot task allocation (MRTA) is essential for scalable and resilient autonomous systems. The Consensus-Based Bundle Algorithm (CBBA) is a widely adopted decentralized baseline. However, its individual task-level bidding is poorly aligned with the min-sum objective of minimizing total team travel distance, leading to suboptimal allocations in spatially distributed environments. This paper introduces the Grouping Auction-Consensus Algorithm (GACA). This decentralized MRTA framework adopts the two-phase auction-consensus architecture of CBBA while fundamentally redesigning its bidding mechanism to reason over groups of spatially proximate tasks. A nearest-neighbor preprocessing step partitions tasks into spatially coherent groups before allocation. Agents then iteratively propose structured group-level actions: claiming unassigned groups, acquiring partial groups, or contesting groups held by other agents. Competing actions are resolved through a consensus phase. Operating in the MT-SR-IA problem class, GACA is evaluated against CBBA using a Mixed-Integer Linear Program as the ground-truth optimality reference. Across four swarm sizes and 4,000 test worlds, GACA achieves a median percent optimality of approximately 97% compared to 81--84% for CBBA, while converging in equal or fewer iterations. A scalability evaluation over 3,280 additional problem instances spanning swarm sizes of 5 to 20 agents and task counts of 10 to 50 confirms that these gains generalize robustly across a wide range of problem configurations.

cs.RO↗

arXiv2026

Auction-Consensus Algorithm with Learned Bidding Scheme for Multi-Robot Systems

Multi-Robot Task Allocation (MRTA) is a central challenge in decentralized multi-agent systems, where teams of robots must cooperatively assign and execute tasks under limited communication while optimizing global performance objectives. Auction-consensus algorithms, such as the Consensus-Based Bundle Algorithm (CBBA), provide scalable decentralized coordination with provable convergence, but rely on hand-crafted greedy scoring functions that often lead to suboptimal task allocations. This paper proposes a learning-enhanced auction-consensus framework in which CBBA's deterministic bidding mechanism is replaced by a neural bidding policy trained using reinforcement learning. Under a centralized training and decentralized execution paradigm, agents learn to compute task bids from partial local observations while retaining the standard auction and consensus phases for decentralized coordination. The learned bidding policy is trained using Proximal Policy Optimization with rewards shaped by proximity to globally optimal solutions obtained via mixed-integer linear programming. Multiple neural architectures are evaluated, including a Neural Additive Model, the Long Short-Term Memory (LSTM) model, and the Set Transformer Model. Experimental results across varying swarm sizes demonstrate that learned bidding policies can improve solution quality over classical CBBA while preserving decentralized execution. The proposed approach highlights the effectiveness of integrating reinforcement learning with classical distributed coordination algorithms, offering a scalable pathway toward higher-quality decentralized multi-robot task allocation.

cs.RO↗

arXiv2024

An Effective Current Limiting Strategy to Enhance Transient Stability of Virtual Synchronous Generator

VSG control has emerged as a crucial technology for integrating renewable energy sources. However, renewable energy have limited tolerance to overcurrent, necessitating the implementation of current limiting (CL)strategies to mitigate the overcurrent. The introduction of different CL strategies can have varying impacts on the system. While previous studies have discussed the effects of different CL strategies on the system, but they lack intuitive and explicit explanations. Meanwhile, previous CL strategy have failed to effectively ensure the stability of the system. In this paper, the Equal Proportional Area Criterion (EPAC) method is employed to intuitively explain how different CL strategies affect transient stability. Based on this, an effective current limiting strategy is proposed. Simulations are conducted in MATLAB/Simulink to validate the proposed strategy. The simulation results demonstrate that, the proposed effective CL strategy exhibits superior stability.

eess.SY↗

arXiv2022

Invariants of SDP exactness in quadratic programming

In this paper we study the Shor relaxation of quadratic programs by fixing a feasible set and considering the space of objective functions for which the Shor relaxation is exact. We first give conditions under which this region is invariant under the choice of generators defining the feasible set. We then describe this region when the feasible set is invariant under the action of a subgroup of the general linear group. We conclude by applying these results to quadratic binary programs. We give an explicit description of objective functions where the Shor relaxation is exact and use this knowledge to design an algorithm that produces candidate solutions for binary quadratic programs.

math.OC↗

arXiv2017

An Attention Mechanism for Answer Selection Using a Combined Global and Local View

We propose a new attention mechanism for neural based question answering, which depends on varying granularities of the input. Previous work focused on augmenting recurrent neural networks with simple attention mechanisms which are a function of the similarity between a question embedding and an answer embeddings across time. We extend this by making the attention mechanism dependent on a global embedding of the answer attained using a separate network. We evaluate our system on InsuranceQA, a large question answering dataset. Our model outperforms current state-of-the-art results on InsuranceQA. Further, we visualize which sections of text our attention mechanism focuses on, and explore its performance across different parameter settings.

cs.CL↗

arXiv2017

Correlative cellular ptychography with functionalized nanoparticles at the Fe L-edge

Precise localization of nanoparticles within a cell is crucial to the understanding of cell-particle interactions and has broad applications in nanomedicine. Here, we report a proof-of-principle experiment for imaging individual functionalized nanoparticles within a mammalian cell by correlative microscopy. Using a chemically-fixed, HeLa cell labeled with fluorescent core-shell nanoparticles as a model system, we implemented a graphene-oxide layer as a substrate to significantly reduce background scattering. We identified cellular features of interest by fluorescence microscopy, followed by scanning transmission X-ray tomography to localize the particles in 3D, and ptychographic coherent diffractive imaging of the fine features in the region at high resolution. By tuning the X-ray energy to the Fe L-edge, we demonstrated sensitive detection of nanoparticles composed of a 22 nm magnetic Fe3O4 core encased by a 25-nm-thick fluorescent silica (SiO2) shell. These fluorescent core-shell nanoparticles act as landmarks and offer clarity in a cellular context. Our correlative microscopy results confirmed a subset of particles to be fully internalized, and high-contrast ptychographic images showed two oxidation states of individual nanoparticles with a resolution of ~16.5 nm. The ability to precisely localize individual fluorescent nanoparticles within mammalian cells will expand our understanding of the structure/function relationships for functionalized nanoparticles.

physics.bio-ph↗

arXiv2016

Open problems in Banach spaces and measure theory

We collect several open questions in Banach spaces, mostly related to measure theoretic aspects of the theory. The problems are divided into five categories: miscellaneous problems in Banach spaces (non-separable $L^p$ spaces, compactness in Banach spaces, $w^*$-null sequences in dual spaces), measurability in Banach spaces (Baire and Borel $\sigma$-algebras, measurable selectors), vector integration (Riemann, Pettis and McShane integrals), vector measures (range and associated $L^1$ spaces) and Lebesgue-Bochner spaces (topological and structural properties, scalar convergence).

math.FA↗

arXiv2012

Combinatorial Excess Intersection

We provide formulas and algorithms for computing the excess numbers of certain ideals. The solution for monomial ideals is given by the mixed volumes of certain polytopes. These results enable us to design specific homotopies for numerical algebraic geometry.

math.CO↗

arXiv2012

Maximum Likelihood Duality for Determinantal Varieties

In a recent paper, Hauenstein, Sturmfels, and the second author discovered a conjectural bijection between critical points of the likelihood function on the complex variety of matrices of rank r and critical points on the complex variety of matrices of co-rank r-1. In this paper, we prove that conjecture for rectangular matrices and for symmetric matrices, as well as a variant for skew-symmetric matrices. To appear in International Mathematics Research Notices.

math.AG↗

arXiv2012

Maximum Likelihood for Matrices with Rank Constraints

Maximum likelihood estimation is a fundamental optimization problem in statistics. We study this problem on manifolds of matrices with bounded rank. These represent mixtures of distributions of two independent discrete random variables. We determine the maximum likelihood degree for a range of determinantal varieties, and we apply numerical algebraic geometry to compute all critical points of their likelihood functions. This led to the discovery of maximum likelihood duality between matrices of complementary ranks, a result proved subsequently by Draisma and Rodriguez.

math.AG↗

arXiv2012

Analytical Solution of the Forward Displacement Problem for Spherical Parallel Manipulators

In this paper, an analytical method that solves the forward displacement problem of several common spherical parallel manipulators (SPMs) is presented. The method uses the the quaternion algebra to restate the problem as a system of four quadrics in four variables and uses an algebraic geometry result by Dixon from 1908 to solve. In addition, a case study is presented for a specific SPM.

math.NA↗

arXiv2011

Bounding the Degree of Belyi Polynomials

Belyi's Theorem states that a Riemann surface, X, as an algebraic curve is defined over an algebraic closure of the rationals if and only if there exists a holomorphic function taking X to the Riemann sphere with at most three critical values (traditionally taken to be zero, one, and infinity). By restricting to the case where X is the Riemann sphere and our holomorphic functions are Belyi polynomials, we define a Belyi height of an algebraic number to be the minimal degree of Belyi polynomials mapping said algebraic number to either zero or one. We prove, for non-zero algebraic numbers with non-zero p-adic valuation, that the Belyi height must be greater than or equal to p using the combinatorics of Newton polygons. We also give examples of algebraic numbers which show our bounds are sharp.

math.NT↗

arXiv2010

The genome is software and evolution is a software developer

The genome is software because it a set of verbal instructions for a programmable computer, the ribosome. The theory of evolution now reads: evolution is the software developer responsible for the existence of the genome. We claim that this setting, whose official name is genetic programming, is necessary and sufficient to discuss all important questions about evolution. A great effort has been made to pass from wording to science, i.e., from naive theories to robust models to predictions to testing for falsification.

q-bio.OT↗

arXiv2009

Recombination and bitsets

A bitset is a set that encodes for a binary number. Bitsets are at the basis of a beautiful theory of recombination with n-loci and here we begin from scratch and advance to include the derivation of the fundamental results about the evolution of gamete frequencies and of disequilibrium measures with and without migration. All techniques have been illustrated and we have invested moreover a great effort to make the mathematics of this work accessible even for students in their first year at the university.

q-bio.PE↗

arXiv2008

Electromagnetism and geometry

This work is an introduction to modern mathematical physics. We begin with Maxwell laws and vector calculus, pass next to consider the action and the Feynman integral in quantum mechanics, next relativity and differential geometry to formulate the electromagnetic laws in intrinsic form. Next we see gravitation to study the covariant derivative. We end with the electromagnetic bundle U(1). It contains the know-how + the know-why. The text is written in Spanish. 340 pps.

math.HO↗

arXiv2006

Simulation in Biology

An invitation to simulation is made into a realizable challenge: the reader is taken from scratch to games with words, to mathematical models, to statistical analysis, to simulation of evolution. No special requirements are needed: we work with the inbuilt Visual Basic language that is attached to Microsoft(R) Excel and Word. The Tex source must be downloaded to copy the code that must be run.

q-bio.PE↗

arXiv2005

The Signature of a Manifold

Let us consider a compact oriented riemannian manifold M without boundary and of dimension n=4k. The signature of M is defined as the signature of a given quadratic form Q. Two different products could be used to define Q and they render equivalent definitions: the exterior product of 2k-forms and the cup product of cohomology classes. The signature of a manifold is proved to yield a topological invariant. Additionally, using the metric, a suitable Dirac operator can be defined whose index coincides with the signature of the manifold. This second version includes corrections and many examples.

math.DG↗